Fujita type exponent for fully nonlinear parabolic equations and existence results

In this paper, we prove that a class of parabolic equations involving a second order fully nonlinear uniformly elliptic operator has a Fujita type exponent. These exponents are related with an eigenvalue problem in all R N and play the same role in blow-up theorems as the classical p ⁎ = 1 + 2 / N introduced by Fujita for the Laplacian. We also obtain some associated existence results.